1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
|
"""
pygments.lexers.tnt
~~~~~~~~~~~~~~~~~~~
Lexer for Typographic Number Theory.
:copyright: Copyright 2006-2021 by the Pygments team, see AUTHORS.
:license: BSD, see LICENSE for details.
"""
import re
from pygments.lexer import Lexer
from pygments.token import Text, Comment, Operator, Keyword, Name, Number, \
Punctuation, Error
__all__ = ['TNTLexer']
class TNTLexer(Lexer):
"""
Lexer for Typographic Number Theory, as described in the book
Gödel, Escher, Bach, by Douglas R. Hofstadter,
or as summarized here:
https://github.com/Kenny2github/language-tnt/blob/master/README.md#summary-of-tnt
.. versionadded:: 2.7
"""
name = 'Typographic Number Theory'
aliases = ['tnt']
filenames = ['*.tnt']
cur = []
LOGIC = set('⊃→]&∧^|∨Vv')
OPERATORS = set('+.⋅*')
VARIABLES = set('abcde')
PRIMES = set("'′")
NEGATORS = set('~!')
QUANTIFIERS = set('AE∀∃')
NUMBERS = set('0123456789')
WHITESPACE = set('\t \v\n')
RULES = re.compile('''(?xi)
joining | separation | double-tilde | fantasy\\ rule
| carry[- ]over(?:\\ of)?(?:\\ line)?\\ ([0-9]+) | detachment
| contrapositive | De\\ Morgan | switcheroo
| specification | generalization | interchange
| existence | symmetry | transitivity
| add\\ S | drop\\ S | induction
| axiom\\ ([1-5]) | premise | push | pop
''')
LINENOS = re.compile(r'(?:[0-9]+)(?:(?:, ?|,? and )(?:[0-9]+))*')
COMMENT = re.compile(r'\[[^\n\]]+\]')
def __init__(self, *args, **kwargs):
Lexer.__init__(self, *args, **kwargs)
self.cur = []
def whitespace(self, start, text, required=False):
"""Tokenize whitespace."""
end = start
try:
while text[end] in self.WHITESPACE:
end += 1
except IndexError:
end = len(text)
if required and end == start:
raise AssertionError
if end != start:
self.cur.append((start, Text, text[start:end]))
return end
def variable(self, start, text):
"""Tokenize a variable."""
if text[start] not in self.VARIABLES:
raise AssertionError
end = start+1
while text[end] in self.PRIMES:
end += 1
self.cur.append((start, Name.Variable, text[start:end]))
return end
def term(self, start, text):
"""Tokenize a term."""
if text[start] == 'S': # S...S(...) or S...0
end = start+1
while text[end] == 'S':
end += 1
self.cur.append((start, Number.Integer, text[start:end]))
return self.term(end, text)
if text[start] == '0': # the singleton 0
self.cur.append((start, Number.Integer, text[start]))
return start+1
if text[start] in self.VARIABLES: # a''...
return self.variable(start, text)
if text[start] == '(': # (...+...)
self.cur.append((start, Punctuation, text[start]))
start = self.term(start+1, text)
if text[start] not in self.OPERATORS:
raise AssertionError
self.cur.append((start, Operator, text[start]))
start = self.term(start+1, text)
if text[start] != ')':
raise AssertionError
self.cur.append((start, Punctuation, text[start]))
return start+1
raise AssertionError # no matches
def formula(self, start, text):
"""Tokenize a formula."""
if text[start] in self.NEGATORS: # ~<...>
end = start+1
while text[end] in self.NEGATORS:
end += 1
self.cur.append((start, Operator, text[start:end]))
return self.formula(end, text)
if text[start] in self.QUANTIFIERS: # Aa:<...>
self.cur.append((start, Keyword.Declaration, text[start]))
start = self.variable(start+1, text)
if text[start] != ':':
raise AssertionError
self.cur.append((start, Punctuation, text[start]))
return self.formula(start+1, text)
if text[start] == '<': # <...&...>
self.cur.append((start, Punctuation, text[start]))
start = self.formula(start+1, text)
if text[start] not in self.LOGIC:
raise AssertionError
self.cur.append((start, Operator, text[start]))
start = self.formula(start+1, text)
if text[start] != '>':
raise AssertionError
self.cur.append((start, Punctuation, text[start]))
return start+1
# ...=...
start = self.term(start, text)
if text[start] != '=':
raise AssertionError
self.cur.append((start, Operator, text[start]))
start = self.term(start+1, text)
return start
def rule(self, start, text):
"""Tokenize a rule."""
match = self.RULES.match(text, start)
if match is None:
raise AssertionError
groups = sorted(match.regs[1:]) # exclude whole match
for group in groups:
if group[0] >= 0: # this group matched
self.cur.append((start, Keyword, text[start:group[0]]))
self.cur.append((group[0], Number.Integer,
text[group[0]:group[1]]))
if group[1] != match.end():
self.cur.append((group[1], Keyword,
text[group[1]:match.end()]))
break
else:
self.cur.append((start, Keyword, text[start:match.end()]))
return match.end()
def lineno(self, start, text):
"""Tokenize a line referral."""
end = start
while text[end] not in self.NUMBERS:
end += 1
self.cur.append((start, Punctuation, text[start]))
self.cur.append((start+1, Text, text[start+1:end]))
start = end
match = self.LINENOS.match(text, start)
if match is None:
raise AssertionError
if text[match.end()] != ')':
raise AssertionError
self.cur.append((match.start(), Number.Integer, match.group(0)))
self.cur.append((match.end(), Punctuation, text[match.end()]))
return match.end() + 1
def error_till_line_end(self, start, text):
"""Mark everything from ``start`` to the end of the line as Error."""
end = start
try:
while text[end] != '\n': # there's whitespace in rules
end += 1
except IndexError:
end = len(text)
if end != start:
self.cur.append((start, Error, text[start:end]))
end = self.whitespace(end, text)
return end
def get_tokens_unprocessed(self, text):
"""Returns a list of TNT tokens."""
self.cur = []
start = end = self.whitespace(0, text)
while start <= end < len(text):
try:
# try line number
while text[end] in self.NUMBERS:
end += 1
if end != start: # actual number present
self.cur.append((start, Number.Integer, text[start:end]))
# whitespace is required after a line number
orig = len(self.cur)
try:
start = end = self.whitespace(end, text, True)
except AssertionError:
del self.cur[orig:]
start = end = self.error_till_line_end(end, text)
continue
# at this point it could be a comment
match = self.COMMENT.match(text, start)
if match is not None:
self.cur.append((start, Comment, text[start:match.end()]))
start = end = match.end()
# anything after the closing bracket is invalid
start = end = self.error_till_line_end(start, text)
# do not attempt to process the rest
continue
del match
if text[start] in '[]': # fantasy push or pop
self.cur.append((start, Keyword, text[start]))
start += 1
end += 1
else:
# one formula, possibly containing subformulae
orig = len(self.cur)
try:
start = end = self.formula(start, text)
except (AssertionError, RecursionError): # not well-formed
del self.cur[orig:]
while text[end] not in self.WHITESPACE:
end += 1
self.cur.append((start, Error, text[start:end]))
start = end
# skip whitespace after formula
orig = len(self.cur)
try:
start = end = self.whitespace(end, text, True)
except AssertionError:
del self.cur[orig:]
start = end = self.error_till_line_end(start, text)
continue
# rule proving this formula a theorem
orig = len(self.cur)
try:
start = end = self.rule(start, text)
except AssertionError:
del self.cur[orig:]
start = end = self.error_till_line_end(start, text)
continue
# skip whitespace after rule
start = end = self.whitespace(end, text)
# line marker
if text[start] == '(':
orig = len(self.cur)
try:
start = end = self.lineno(start, text)
except AssertionError:
del self.cur[orig:]
start = end = self.error_till_line_end(start, text)
continue
start = end = self.whitespace(start, text)
except IndexError:
try:
del self.cur[orig:]
except NameError:
pass # if orig was never defined, fine
self.error_till_line_end(start, text)
return self.cur
|
